# Translations:Causality and stability of digital systems/36/en

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We now divide the poles into two sets: those with magnitude greater than one, which we designate as , , , and those with magnitude less than one, which we designate as , , ,. For the first set, we pick the regions as the regions of convergence. For the second set, we pick the regions as the regions of convergence. Thus, all the regions include the unit circle. It follows that the stable impulse response is the two-sided signal given by